Have seen this a few times already but apparently even with the
latest 7.1.2 version, the IDE is still unable to rename a
project correctly.
Here are the steps to reproduce:
1) Right click on Header Files (under the Project) -> Add
Existing Items from Folders -> Add, select a folder
containing header files.
2) Right click on Project -> Rename.
3) Enter new Project Name, and click on "Also Rename Project
Folder".
4) Hit Rename button.

Once the above three steps are done, if you have header files
added to the project before the rename, the IDE would indicate
the #include files not found on both the Editor (with the red
wriggly lines), and in the Project Tree (with an exclaimation
mark).

Turns out the issue was the IDE also renamed the path of these
files as from "../../<directory>" to
"/../../<directory>". This can be viewed from:
1) Right click on Project -> Properties.
2) Click on C++ Compilers, hit on the "..." button for Included
Directories.
Same thing also if click on Linker, hit on the "..." button
for Additional Library Directories.